SOSTOOLS: Sum of squares optimization toolbox for MATLAB

2002

597 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/805cb4756b35eec0ed72fa2593653ad87942ea16

Citations in the corpus

• Feedback Systems: An Introduction for Scientists and Engineers (2008, unknown): “Recent results using sum-of-squares methods have provided systematic approaches for finding Lyapunov systems [167].”
• Layering as Optimization Decomposition: A Mathematical Theory of Network Architectures (2007, unknown): “, sum-of-squares programming [108], [109] and geometric-signomial programming [19], [32], although some aspects of these techniques are not well understood (e.”
• Control Barrier Functions: Theory and Applications (2019, unknown): “There exist efficient computational toolboxes that convert certain SOS constraints into semidefinite programs such as [46].”
• Review on computational methods for Lyapunov functions (2015, unknown): “For further information see its user’s guide Papachristodoulou, Anderson, Valmorbida, Pranja, Seiler, and Parrilo 2013 [185].”
• Periodic event-triggered control for nonlinear systems (2013, unknown): “3SOSTools ([17]) was used to compute ςi andχi for i ∈ {1, 2, 3}.”
• LMI Techniques for Optimization Over Polynomials in Control: A Survey (2010, unknown): “An interesting strategy reformulates the above problem into the problem of establishing whether a homogeneous polynomial is positive [5].”
• A survey on stability analysis of discrete-time piecewise affine systems (2005, unknown): “• It was observed that the numerical problems associated to the SOS approaches occur regardless of SOS (Löfberg, 2004; Prajna et al., 2004) and SDP (Sturm, 1999; Toh et al.”
• Lyapunov conditions for input-to-state stability of impulsive systems (2008, unknown): “The candidate Lyapunov function (37) was found numerically, using the SOSTOOLS MATLAB toolbox [20].”
• LQR-trees: Feedback Motion Planning via Sums-of-Squares Verification (2010, unknown): “Freely available libraries, including SOSTOOLS (Prajna et al. 2004a) and the Systems Polynomial Optimization Toolbox (Megretski) make performing these computations in MATLAB feasible.”
• Detecting global optimality and extracting solutions in GloptiPoly (2003, unknown): “Note that there exist a dual approach to build hierarchy of LMI relaxations, based on real algebraic geometry and sum-of-squares (SOS) decompositions of positive polynomials, see [16] for the theory and [18] for a Matlab/SeDuMi implementation.”
• A sampling approach to finding Lyapunov functions for nonlinear discrete-time systems (2016, unknown): “A solution to avoid non–convex problems is given for polynomial dynamics by sum–of–squares methods for testing global asymptotic stability [6], [7] or, for general nonlinear dynamics, by piecewise affine approximations of Lyapunov functions over simplices [8], [9].”
• Finite-time regional verification of stochastic non-linear systems (2011, unknown): “Much of the continuous-state verification research has focused on non-linear systems with Gaussian and switching noise (Prajna et al. 2004a; Yang et al. 2009).”